Originally Posted by

**thekrown** Okay, I think I got this. My teacher and textbook use different notations, or there are different notations so the examples I have in class are not exactly as those in the textbook but I think I got it.

With

x = -5 - 4t

y = 1 - t

z = 3 +2t

and x + 2y + 3z - 9 = 0

I can sub the x,y,z into the equation. Then in order to find out if it is parallel I have this note:

at + b = 0

a = 0, then b = 0

If we get 0 = 0 then any t is a solution and is parallel.

If we get b = 0 or b =/= 0 then perpendicular.

In this problem, we get

(-5-4t) + 2(1-t) + 3(3+2t) - 9 = 0

-5 -4t + 2 - 2t + 9 + 6t - 9 = 0

Since t = 0 then a = 0 and so b is 0. So by the above notes we should get 0 = 0. I actually get -3=0.

Following my notes, I would say this is parallel. I just don't understand why I get -3 = 0.